An Information Geometry Problem in Mathematical Finance  Imre Csiszár, Michel Broniatowski, Thomas Breuer

Author(s): Imre Csiszár, Michel Broniatowski, Thomas Breuer
DOI URL: http://dx.doi.org/10.1007/9783319250403_47
Video: not available
Slides: Breuer_Information geometry finance.pdf
Presentation: https://www.see.asso.fr/node/14346
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
Familiar approaches to risk and preferences involve minimizing the expectation EIP(X) of a payoff function X over a family _ of plausible risk factor distributions IP. We consider _ determined by a bound on a convex integral functional of the density of IP, thus _ may be an Idivergence (relative entropy) ball or some other fdivergence ball or Bregman distance ball around a default distribution IPo. Using a Pythagorean identity we show that whether or not a worst case distribution exists (minimizing EIP(X) subject to IP__), the almost worst case distributions cluster around an explicitly specified, perhaps incomplete distribution. When _ is an fdivergence ball, a worst case distribution either exists for any radius, or it does/does not exist for radius less/larger than a critical value. It remains open how far the latter result extends beyond fdivergence balls.